On the N=2 superconformal index and eigenfunctions of the elliptic RS model

TL;DR

This paper introduces a sequence of superconformal indices for N=2 theories, providing a recursive method to compute them and linking this to eigenfunctions of the elliptic Ruijsenaars-Schneider model, advancing both physics and mathematics.

Contribution

It proposes a new sequence of superconformal indices and a recursive technique to determine them, connecting physical indices with mathematical eigenfunctions.

Findings

Defined an infinite sequence of superconformal indices I_n.

Developed a recursive method for theories of class S.

Established a perturbative algorithm for eigenfunctions of the elliptic RS model.

Abstract

We define an infinite sequence of superconformal indices, I_n, generalizing the Schur index for N=2 theories. For theories of class S we then suggest a recursive technique to completely determine I_n. The information encoded in the sequence of indices is equivalent to the N=2 superconformal index depending on the maximal set of fugacities. Mathematically, the procedure suggested in this note provides a perturbative algorithm for computing a set of eigenfunctions of the elliptic Ruijsenaars-Schneider model.